On a Multiple-Scales Analysis of Multilateral Phenomena in Semiconductor Lasers

A mathematical model describing the coupling of electrical and optical effects in the active region of a realistic semiconductor laser medium is introduced. The weakly nonlinear analysis which follows gives rise to a leading-order problem describing three lateral modes. At the next order, the secularity conditions exhibit competition for photons and modal interaction. By making further assumptions, a partially lumped model is deduced which has no counterpart in the existing literature; this simplified system consists of one parabolic and six first-order hyperbolic partial differential equations. Predictions of this partially lumped model are compared with experimental observations.